1. Field of Invention
This invention relates to apparatus and method for controlling machinery for manufacturing paper; and more particularly to improvements in such apparatus and method whereby the uniformity and quality of the manufactured paper are increased.
2. Description of the Prior Art
A controller for paper making machines is disclosed, for example, in Japan Laid-Open Application 63-75,197, filed by the same inventors as herein.
FIG. 1 is a perspective view of a paper making machine, wherein raw materials discharged from a head box 5 are waterdrawn through a wire part 8 to eliminate water; then pressed by a press part 9 into a predetermined thickness; then dried through a drying part 15; then given gloss at the surface thereof through a calender 11; and then wound by a reel or roll 12. Head box 5 is provided with a slicing device (herein sometimes "slice") comprising a slice lip 6 for discharging raw materials and a slice bolt 7 for adjusting the opening of slice lip 6 in the cross paper direction, to have a constant pitch for example of several 10s of number. A white water silo 3 receives white water drawn by wire part 3, which is then returned to head box 5 by a pump 4. At the entrance of pump 4, the raw materials or stock in stock or stuff box 1 are injected through a stock control valve 2.
A sensor 14 for measuring the basis weight and moisture percentage of the paper moves reciprocally along a frame 13 provided between calender 11 and reel 12 to measure the paper width. Examples of a sensor for measuring the moisture percentage are disclosed in U.S. Pat. No. 4,315,150 and U.S. Pat. No. 4,620,146. The data of paper width is called the profile.
The controller 16 receives as inputs the measured basis weight profile from sensor 14 and operates slice bolt 7 so that the measured basis weight profile becomes equal to a desired basis weight profile , in order to control the stroke of slice lip 6. With regard to the moisture percentage, a measured moisture percentage profile is inputted to a controller and the steam of drying part 15 is controlled thereby so that such measured moisture percentage profile becomes equal to a desired moisture percentage profile. Adjusting departures from the desired value of average value of basis weight is carried out by controlling the stroke of stock control valve 2.
FIG. 2 is a functional block diagram depicting a paper making machine controller, wherein a profile arithmetic means 32 computes a deviation between a measured profile signal measured by sensor 14, and a predetermined desired profile and sets up correspondence between the measured profile signal and an actually operated slice by referring to a signal from the corresponding position means 34, and thereby obtain control deviation .rho.(k) of each slice (k).
The measured profile is obtained, for example, by providing a total of 360 measuring points in the cross machine direction and a mean value of adjacent six points is obtained for smoothing purpose. The desired profile makes a slightly large basis weight at the center, for example, but makes a slightly small basis weight at both sides to stably take up the paper with reel 12. Corresponding position means 34 describes correspondence between the measuring points of the measured profile signal and slice and predetermines it with theoretical formulas and experiments. A slice manipulated variable arithmetic means 38 obtains a slice manipulated signal in this control period and outputs a differential manipulated value .DELTA..vertline.U(k) and operates as a core part of the controller 16. An output controller means 60 adds the differential manipulated value .DELTA..vertline.U(k) of each slice obtained by the slice manipulated variable arithmetic means 38 to the preceding manipulated variable .vertline.U(k) and outputs such value as the manipulated .vertline.U(k) of this time. For example, this value is determined to be a natural number multiplied by the scanning period of the sensor or is determined with reference ,to a time constant of the paper making machine or arithmetic capability of the controller. For example, when the scanning period of the sensor 14 is 30 seconds, the control period of output controlling means 60 is determined to be every two minutes. Manual manipulation by skilled operators of the slice manipulated variable arithmetic means 38 is used in many paper making factories.
FIG. 3 is a structural block diagram of a paper making machine control system focusing on controller 16 and the control conditions. Correspondence to the slice is set up for simplification of explanation. In controller 16, a manipulated variable is obtained from deviation e(k) between the desired value, that is a preset value indicated as y(k), and basis weight profile y(k), which is fed back from the right side as depicted. With this manipulated variable, slice bolt 7 is adjusted and the basis weight profile which changes thereby is fed back. The deviation e(k) is controlled to become close to zero.
The manipulated variable in such control system is a slice lip stroke pattern (U.sub.1, . . . , U.sub.N) and the controlled variable is a basis weight profile (y.sub.1, . . . , y.sub.N). A plant can be approximated by the first-order lag and cross machine direction interference but it can be indicated as follows with the S domain of the Laplace transformation. EQU Y(S)={k/(1+T.sub.S } AU(S) (1)
wherein, Y(S) is the Laplace transformation of vector y.vertline. (t), and y.vertline. (t) is the transposed matrix (indicated as [y.sub.1 (t), . . . , y.sub.N (t)].sup.T) of the matrix [Y.sub.1 (t), . . . , y.sub.N (t)]. U(S) is the Laplace transform of vector ui (t), wherein ui (t) is the transposed matrix [u.sub.1 (t), 111, u.sub.N (t)], k is the gain, t is the time, and T is a time constant, and A is the interference matrix (N.times.N), which satisfies the following relationship. ##EQU1##
The conventional control rule combines the arithmetic operation considering interference and PI(proportion/integration) and considering first order lag and it can be be indicated as follows using a scattering time and type of speed. EQU .DELTA..vertline.U(k)=K.sub.p M .DELTA.e(k)+K.sub.1 Me(k) (2)
wherein k is the scattering time, .vertline.U(k) is the scattering time slice lip stroke vector, .DELTA..vertline.U(k) is the differential value, e(k) is the control deviation vector of the scattering time, e.sub.j (k) is the control deviation, .DELTA.e(k) is the differential value, respectively, and satisfying the following relationships. ##EQU2## wherein K.sub.p is the proportional gain, K.sub.i is the integration gain, M is the N.times.N matrix considering the interference.
Next, the operation will be explained. The arithmetic operation considering the interference is carried out in arithmetic unit 22 for the deviation (i.e. control deviation) ek) of the desired value obtained at the adding point 21 and the controlled value. The result is indicated by the following formula. EQU e'(k)=[e'.sub.1 (k), . . . , e'.sub.N (k)].sup.T
In this case, the following formula is set up between e'(k) and e(k). EQU e'(k)=Me(k) (3)
Both e'(k) and .DELTA.e'(k) are inputted to controller 25. The differential value .DELTA.e'(k) is a differential of the output e'(k-1) of the arithmetic unit 22 and a previous output e'(k-1) of the arithmetic unit through a buffer 23 obtained at adding point 24 and is indicated by the following formula. EQU .DELTA.e'(k)=e'(k)-e'(k-1)
The controller 25 also conducts the PI arithmetic operation indicated by the following formula. EQU .DELTA..vertline.U(k)+K.sub.p .DELTA.e'(k)+K.sub.1 e'(k) (4)
This arithmetic operation can also be expressed by the scalar arithmetic operation for each element of vector as shown below. EQU .DELTA.u.sub.i (k)=K.sub.p .DELTA.e'.sub.1 (k)+K.sub.1 e'.sub.i (k) (5)
wherein i is 1 to N.
The adder 26 adds an output .DELTA..vertline.U(k) from controller 25 to the preceding slice lip stroke vector of itself and outputs the result as the slice lip stroke vector .vertline.U(k) of this time. This slice lip stroke vector .vertline.U(k) is applied to the plant 28 as the manipulated variable .vertline.U(t) through a zero order hold circuit 27.
An output, namely, the basis weight profile, y(t) of plant 28 is extracted through a sampler 29 which conducts sampling in each k period and is fed back to adding point 21.
The plant is ideally expressed by formula (1), but, actually, includes complicated nonlinear characteristics. Thus, a problem arises in that the linear control indicated by formula (2) is insufficient.
The conventional controller encounters many problems, some examples are those listed above and as follows.
FIGS. 4(A) and 4(B) are diagrams for explaining a sawtooth wave between the slices, with FIG. 4(A) depicting the waveform before manipulation, and FIG. 4(B) depicting the waveform after the manipulation. The horizontal axis indicates the width direction of the paper, while the vertical axis indicates the position of the measuring end where influence of the slice appears most distinctively (called the corresponding position). The arrow indicates manipulation of the relevant slice. In order to eliminate the sawtooth wave between the slices, the slices at both ends are manipulated by providing two slices therebetween (see FIG. 4(A)). However, the bottom part of the basis weight is generated at the position of the manipulated slice and the sawtooth wave is inversely increased in some cases (see FIG. 4(B)).
Since the process is complicated, ideal response of the basis weight profile often does not appear for the manipulation of the slice. Particularly when many slices are manipulated at one time, the basis weight profile is disturbed and manual intervention of a skilled operator is often required.
When the process is very disturbed, such as when a product is changed remarkably or the paper making machine operation is initiated, a longer time is required to converge the basis weight profile up to a desired quality and a large amount of paper is lost until the paper is brought up to the desired quality.
As another problem, the slice may sometimes become permanently distorted toward excessive bending and when a permanent magnet is once generated, the lip stroke can no longer be adjusted even when the slice bolt is manipulated. Thus, it is necessary to restrict manipulation variable by providing a limit to the stroke difference between adjacent slice bolts. However, according to the conventional machine, if the basis weight is uniform the lip stroke pattern of the slice is disturbed and exceeds the adjacent lip stroke limit. The influence of stress distribution of raw material output and shape of the slice lip is controlled within a constant range but excessive disturbance is a problem for the protection of the slice.
Moreover, the corresponding position between the slice and the measuring point of the sensor is also changed delicately for each change of process condition. Thus, the content of the corresponding position means 34 does not always match the current process. This creates a problem in that any manipulation of the slice may not result in a uniform basis weight profile as desired.
Thus, it can be readily appreciated that the prior art method and apparatus for controlling paper making leave room for improvement.